No brainer if you are in school but out of school and if some one asks you this question, can you answer it?

Finding factors:{If you are preparing for GMAT this should give you a quick review of what factors are?}

One easy way is through prime numbers as they make it easy to find the factors of a number.

What is a prime number : A number is prime if it cannot be divided evenly by anything except itself and 1. For example, 5 is aprime number, because the only factors of 5 are

1 * 5 = 5

Let’s consider a number like 121:

how many factors does 121 have?

121 = 11 X 11, 11 is prime number

So prime factors of 121 are 1, 11 and 121

Let’s consider a number like 72 that you want to find factors of It’s even, so it’s divisible by 2:

72 = 2 * 36

Now, what about 36? That’s also even, so it’s divisible by 2:

72 = 2 * 2 * 18

What about 18? That’s divisible by 2:

72 = 2 * 2 * 2 * 9

What about 9? That’s not divisible by 2, but it is divisible by 3:

72 = 2 * 2 * 2 * 3 * 3

And 3 is prime. So what we’ve done here is find the ‘prime factors’ ofthe number 72.

How does this help us find all the factors of 72? Well, if a numberis a factor of 72, and it’s not one of these prime factors, then itmust be a product of two or more prime factors. So we can find all thefactors of 72 by looking at all the ways we can group these primefactors:

2 * 2 = 4 pairs 2 * 3 = 6 3 * 3 = 9

2 * 2 * 2 = 8 2 * 2 * 3 = 12 triplets 2 * 3 * 3 = 18

2 * 2 * 2 * 3 = 24 product of four prime factors 2 * 2* 3 * 3 = 36

So the factors of 72 are

1 A factor of everything.

2, 3 The distinct prime factors.

4, 6,9 Products of two prime factors.

8,12,18 Products of three prime factors.

24,36 Products of three prime factors.

72 Product of all the prime factors.

Now

1,2,3,4,6,8,9,12,18,24,36,72

Factors vs Multiples basics

Factors Finite number of factors for any whole number Most factors are smaller than number – largest is number itself

MultiplesInfinite number of multiplesMost multiples larger than number, smallest is number itself